Relationships between category theory and functional programming with an application

Abstract

The most recent studies in mathematics are concerned with objects, morphisms, and the relationship between morphisms. Prominent examples can be listed as functions, vector spaces with linear transformations, and groups with homomorphisms. Category theory proposes and constitutes new structures by examining objects, morphisms, and compositions. Source and target of a morphism in category theory corresponds to input and output in programming language. Thus, a connection can be obtained between category theory and functional programming languages. From this point, this paper constructs a small category implementation in a functional programming language called Haskell.